Radio frequency impairments compensator for broadband quadrature-conversion architectures

ABSTRACT

A Radio Frequency Impairments (RFI) compensator and a process to remove RFI is disclosed. The RFI compensator including: a conjugator to conjugate a signal {tilde over (x)}[n] to provide a signal {tilde over (x)}*[n]; and a filter to apply coefficients that equalize a linear distortion of the signal {tilde over (x)}[n] and reject an interfering image of the signal {tilde over (x)}*[n]. The signal {tilde over (x)}[n] may be a single wideband carrier or may include multiple carriers at different carrier frequencies.

FIELD

A system and method to jointly suppress a Direct Current (DC) offset andremove radio-frequency (RF) impairments encountered inquadrature-conversion is disclosed. The method and system copeparticularly well with strong in-phase/quadrature (IQ) imbalance that isfrequency-selective in broadband applications, while toleratingfrequency error between mixers at a transmitter and a receiver. Themethod and system are effective for a single wideband carrier signal ora signal including multiple carriers at different carrier frequencies.Moreover, the system and method are adaptive and do not require a prioriknowledge about the RF impairments impulse response.

BACKGROUND

A quadrature frequency conversion architecture is used in moderncommunications systems. It is responsible for a frequency translation,up at the transmitter-side and down at the receiver-side, between abaseband and the Radio Frequency (RF) of a carrier. Special cases ofquadrature-conversion architectures include zero-Intermediate Frequency(IF) and low-IF converters. Analog elements are used for frequencyconversion to implement mixers, filters, amplifiers, and oscillators.However, the imperfections and finite tolerance of analog elementsinduce mismatch between the in-phase/quadrature (IQ) branches of theconverters.

A mismatch between the phase and gain of the IQ mixer arms createsimbalance that is constant over the signal band. The mismatch betweenthe analog anti-aliasing filters in the IQ arms causes an imbalance thatis frequency-selective. Also, there can exist a Direct-Current (DC)offset on each arm resulting from the Local Oscillator (LO) leakage. Thepresence of In-phase Quadrature Imbalance (IQI) and DC offsetsignificantly degrades system performance.

This problem is worse when wideband signals with high-order modulationsare used. Maintaining match of anti-aliasing filters over a wide rangeof frequencies is very difficult in the analog domain. The difficultiesincrease the cost of manufacture and cause delays in chip design time.As such, the problem of frequency-selective IQI that is strong and haslarge memory span needs to be addressed effectively in next-generationcommunications systems.

FIG. 1 illustrates a prior art quadrature-conversion system operating ona bandpass input r(t) and providing an output x(t).

The output x(t) includes imperfections from the analog RF elements, suchas h_(I)(t) and h_(Q)(t). A mismatch in a gain g and a phase φ betweenan in-phase arm and a quadrature arm of a LO mixer induce afrequency-independent IQ imbalance, whereas the mismatch between theanalog anti-aliasing filters h_(I)(t) and h_(Q)(t) contribute tofrequency-selective IQ imbalance. The filter h(t) is common to the twopaths. For broadband systems, the difference between these anti-aliasingfilters h_(I)(t) and h_(Q)(t) in each of the IQ arms becomes significantas it is difficult to maintain a match over a large frequency range inthe analog domain. The LO carrier leakage induces a DC offset α_(DC,I)and α_(DC,Q) in each arm separately. Furthermore, there is anunavoidable frequency error, denoted as δ_(ƒ), between the mixers placedat the transmitter and the receiver. The frequency error harmsperformance if not addressed properly.

SUMMARY

This Summary is provided to introduce a selection of concepts in asimplified form that is further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used to limit the scope of the claimed subject matter.

The present teachings, jointly or singly, suppress the DC offset andremove an imbalance encountered in quadrature-conversion systems, copingparticularly well with in-phase/quadrature (IQ) imbalance that is strongand frequency-selective in broadband applications. This is done whiletolerating frequency error that exists between mixers placed at atransmitter and a receiver. The present teachings are adaptive and donot depend upon a priori knowledge about an RF impairments impulseresponse. In some embodiments, the present teachings operate asdata-aided initially, for example, at the factory. In some embodiments,the present teachings operate in decision-directed mode, for example,during normal operation without requiring training data at or from agateway. In some embodiments, a computation of the coefficients for thecompensation scheme is done iteratively without requiring any matrixinversion, as matrix inversion is computationally cumbersome and mayintroduce performance instability. In some embodiments, the coefficientsare computed directly without requiring transformation between time andfrequency domains. This may reduce computational needs. Significantgains are demonstrated when compared with systems that do not use thepresent teachings.

A Radio Frequency Impairments (RFI) compensator is disclosed. The RFIcompensator including: a conjugator to conjugate a signal {tilde over(x)}[n] to provide a signal {tilde over (x)}*[n]; and a filter to applycoefficients that equalize a linear distortion of the signal {tilde over(x)}[n], and reject an interfering image of the signal {tilde over(x)}*[n].

A process to compensate for Radio Frequency Impairments (RFI) isdisclosed. The process including: conjugating a signal {tilde over(x)}[n] to provide a signal {tilde over (x)}*[n]; and filtering byapplying coefficients that equalize a linear distortion of the signal{tilde over (x)}[n] and reject an interfering image of the signal {tildeover (x)}*[n].

Additional features will be set forth in the description that follows,and in part will be apparent from the description, or may be learned bypractice of what is described.

DRAWINGS

In order to describe the manner in which the above-recited and otheradvantages and features may be obtained, a more particular descriptionis provided below and will be rendered by reference to specificembodiments thereof which are illustrated in the appended drawings.Understanding that these drawings depict only typical embodiments andare not, therefore, to be considered to be limiting of its scope,implementations will be described and explained with additionalspecificity and detail through the use of the accompanying drawings.

FIG. 1 illustrates a prior art quadrature-conversion system operating ona bandpass input r(t) and providing an output x(t).

FIG. 2 illustrates a baseband model of a quadrature conversion channelwith Radio Frequency Impairments (RFI) according to various embodiments.

FIG. 3 illustrates an RFI compensator in normal operation mode accordingto various embodiments.

FIG. 4 illustrates an RFI compensator in training operation modeaccording to various embodiments.

FIG. 5A illustrates real part of an impulse response of an RFI channelg₁[n] associated with a received signal according to variousembodiments.

FIG. 5B illustrates imaginary part of an impulse response of an RFIchannel g₁[n] associated with a received signal according to variousembodiments.

FIG. 6A illustrates real part of an impulse response of an RFI channelg₂[n] associated with image of a received signal according to variousembodiments.

FIG. 6B illustrates imaginary part of an impulse response of an RFIchannel g₂[n] associated with image of a received signal according tovarious embodiments.

FIG. 7 illustrates a representative transfer function of compensationfilters w₁[n] and w₂[n] at the end of training for a RFI compensatoraccording to various embodiments.

FIG. 8A illustrates a noiseless scatter plot of an output of a receiveRoot-Raised Cosine (RRC) filter without a RFI compensator according tovarious embodiments.

FIG. 8B illustrates a noiseless scatter plot of an output of a receiveRRC filter with an RFI compensator according to various embodiments.

FIG. 9 illustrates a simulated Mean Squared Error (MSE) at E_(s)/N₀=15dB with and without an RFI compensator according to various embodiments.

FIG. 10 illustrates a signal demodulation including an RFI compensatoraccording to various embodiments.

FIG. 11A illustrates a multi-carrier signal demodulation including aplurality of RFI compensators according to various embodiments.

FIG. 11B illustrates a multi-carrier signal demodulation including anRFI compensator according to various embodiments.

FIG. 12 illustrates a process for RFI compensation according to variousembodiments.

Throughout the drawings and the detailed description, unless otherwisedescribed, the same drawing reference numerals will be understood torefer to the same elements, features, and structures. The relative sizeand depiction of these elements may be exaggerated for clarity,illustration, and convenience.

DETAILED DESCRIPTION

Embodiments are discussed in detail below. While specificimplementations are discussed, it should be understood that this is donefor illustration purposes only. A person skilled in the relevant artwill recognize that other components and configurations may be usedwithout parting from the spirit and scope of the subject matter of thisdisclosure.

The terminology used herein is for describing particular embodimentsonly and is not intended to be limiting of the present disclosure. Asused herein, the singular forms “a,” “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. Furthermore, the use of the terms “a,” “an,” etc. does notdenote a limitation of quantity but rather denotes the presence of atleast one of the referenced item. The use of the terms “first,”“second,” and the like does not imply any particular order, but they areincluded to either identify individual elements or to distinguish oneelement from another. It will be further understood that the terms“comprises” and/or “comprising”, or “includes” and/or “including” whenused in this specification, specify the presence of stated features,regions, integers, steps, operations, elements, and/or components, butdo not preclude the presence or addition of one or more other features,regions, integers, steps, operations, elements, components, and/orgroups thereof. Although some features may be described with respect toindividual exemplary embodiments, aspects need not be limited theretosuch that features from one or more exemplary embodiments may becombinable with other features from one or more exemplary embodiments.

The present teachings achieve a high data rate in broadbandcommunication systems while using cost-effective integratedquadrature-conversion for frequency translation between baseband andradio frequency (RF), and vice versa. The present teachings compensatefor residual impairments induced by imperfections of analog RFcomponents. In some embodiments the present teachings address a strongfrequency-selective IQ imbalance having a large time span. The frequencyselective In-phase/Quadrature (IQ) imbalance occurs as maintaining amatch of anti-aliasing filters in the IQ branches of a converter over awide range of frequencies is very difficult and costly in the analogdomain. The present teachings can tolerate the unavoidable frequencyerror of RF mixers.

FIG. 2 illustrates a baseband model of a quadrature conversion channelwith Radio Frequency Impairments (RFI) according to various embodiments.

Let {tilde over (z)}[n] be the discrete-time baseband representation ofthe input signal without imperfections and let {tilde over (x)}[n] bethe discrete-time baseband signal that includes RF impairments such asIQ imbalance, frequency-independent and frequency-selective, a DC offsetand frequency error. A mathematical derivation (not shown) provides that{tilde over (x)}[n] is given as (* denotes convolution, superscript (.)*denotes conjugation):

{tilde over (x)}[n]=g ₁[n]*({tilde over (z)}[n]·e ^(j2πδ) ^(ƒ) ^(·nT)^(s) )+g ₂[n]*({tilde over (z)}[n]·e ^(j2πδ) ^(ƒ) ^(·nT) ^(s))*+(α_(DC,I) +jα _(DC,Q))

g ₁[n]=h[n]*(h ₁[n]+h _(Q)[n]·g·e ^(−jφ))/2

g ₂[n]=h[n]*(h ₁[n]−h _(Q)[n]·g·e ^(+jφ))/2

FIG. 2 illustrates a discrete-time baseband model 200 of a signal withRF impairments that are induced by quadrature-conversion system of theprior art (see FIG. 1). In FIG. 2, a filter g₁[n] represents and RFimpairments impulse response associated with a signal {tilde over(z)}[n]; whereas a filter g₂[n] represents in RF impairments impulseresponse associated with a interfering mirror image {tilde over (z)}*[n]of signal {tilde over (z)}[n]. The baseband model 200 suggests theteachings disclose herein.

FIG. 3 illustrates an RFI compensator in a normal operation modeaccording to various embodiments.

FIG. 3 illustrates a compensator 300. Let {tilde over (x)}[n] be adiscrete-time baseband signal that includes RF impairments such as IQimbalance, frequency-independent and frequency-selective, a DC offsetand frequency error. The compensator 300 includes two arms. A first arm310 involves the signal {tilde over (x)}[n] and a second arm 312involves a mirror image of signal {tilde over (x)}[n], {tilde over(x)}*[n] resulting from a conjugation. A conjugator 306 may provide{tilde over (x)}*[n]. The filters 308 apply coefficients w₁[n] and w₂[n]to equalize a linear distortion in the signal {tilde over (x)}[n] and tosimultaneously reject the interfering mirror image {tilde over (x)}*[n]respectively. An adder 302 adds a complex term β to an output of thefilters 308 to suppress a DC offset. Further, a complex mixer 304 isthen applied to remove a frequency error. The filters w₁[n] and w₂[n],the complex term β are unknown and calculated as illustrated inexemplary FIG. 4. In some embodiments, an estimated frequency error,e^(j2π{circumflex over (δ)}) ^(ƒ) ^(·nT) ^(s) , is assumed and applied.In exemplary embodiments, the signal {tilde over (x)}[n] may be theoutput of an analog to digital converter (not shown) at a receiver. Inexemplary embodiments, the output of the mixer {tilde over (y)}[n] maybe provided to a demodulator (not shown) at a receiver.

In exemplary embodiments, the filter w₁[n] is not present and filterw₂[n] incorporates the inverse of g₁[n]. This assumes that filter g₁[n]is known, and a mapping between time and frequency domains to providethe inverse and demands higher number of filter taps for itsimplementation, as the inverse is in principle an Infinite-ImpulseResponse (IIR) filter. In addition, this may leave a residualinter-symbol interference in the signal {tilde over (y)}[n] that may beremoved later in the demodulation chain.

FIG. 4 illustrates an RFI compensator in training operation modeaccording to various embodiments.

A compensator 400 can compute filter coefficients and DC offsetsuppression term. The computation of the filter coefficients and DCoffset suppression term, i.e., w₁[n], w₂[n], and β, is performed by astochastic gradient-based technique that may iteratively arrive at thesolution without a priori knowledge of the RF impairment parameters. Insome embodiments the computation may avoid using a matrix inversiontechnique.

In some embodiments, the coefficients are estimated jointly to drive theRF impairments toward zero in a least-squares sense. To this end, astacked construction is used in forming the vector c by stacking vectorsrelating to the filter coefficients and DC-offset parameter as

${\underset{\_}{c} = \begin{bmatrix}\begin{matrix}{\underset{\_}{w}}_{1} \\{\underset{\_}{w}}_{2}\end{matrix} \\\beta\end{bmatrix}},$

as where w ₁=[w₁[0], w₁[1], . . . , w₁[L₁−1]]^(T) and w ₂=[w₂[0], w₂[1],. . . , w₂[L₂−1]]^(T) are the coefficients for the signal andmirror-image filters with memory span L₁ and L₂, respectively. Thecorresponding input vector to the compensator 400 is

${\underset{\_}{\overset{\sim}{x}}\lbrack n\rbrack} = \begin{bmatrix}{{\underset{\_}{\overset{\sim}{x}}}_{1}\lbrack n\rbrack} \\{{\underset{\_}{\overset{\sim}{x}}}_{2}\lbrack n\rbrack} \\1\end{bmatrix}$

where {tilde over (x)} ₁[n]=[{tilde over (x)}[n], {tilde over (x)}[n−1],. . . , {tilde over (x)}[n−L₁+1]]^(T) and {tilde over (x)} ₂[n]=[{tildeover (x)}*[n], {tilde over (x)}*[n−1], . . . , {tilde over(x)}*[n−L₂+1]]^(T). The output of the stacked construction ismathematically expressed as {tilde over (y)}[n]=c ^(T)·{tilde over(x)}[n].

In exemplary embodiments, the present teachings and compensator 400address the frequency offset in training mode. As shown in FIG. 4, aninput signal 404 {tilde over (x)}[n] and a known or reference signal 402{tilde over (z)}[n] can be used to determine an error signal 412 e[n]. Aconjugator 408 may provide a signal {tilde over (x)}*[n].

The known signal 402 represents a baseband signal with no IQ imbalance.The known signal 402 is modified by a complex mixer 406e^(j2π{circumflex over (δ)}) ^(ƒ) ^(·nT) ^(s) to experience similarphase rotation as the input signal 404. If not addressed properly, afrequency error creates a mismatch between the imbalance channel that istrained for versus that to which it is applied, thus harmingperformance. In exemplary embodiments, an estimate of the frequencyerror e^(j2π{circumflex over (δ)}) ^(ƒ) ^(·nT) ^(s) may be obtained bysending a test tone through the imbalance channel and then extractingthe estimate as the slope of the best line formed by the phasemeasurements.

The error signal {tilde over (e)}[n] can then be calculated based on anoutput of the complex mixer 406 and a stacked output as

$\begin{matrix}{{\overset{\sim}{e}\lbrack n\rbrack} = {{{\overset{\sim}{z}\lbrack n\rbrack} \cdot e^{j\; 2\pi \; {{\hat{\delta}}_{f} \cdot {nT}_{s}}}} - {\overset{\sim}{y}\lbrack n\rbrack}}} \\{= {{{\overset{\sim}{z}\lbrack n\rbrack} \cdot e^{j\; 2\pi \; {{\hat{\delta}}_{f} \cdot {nT}_{s}}}} - {{\underset{\_}{c}}^{T} \cdot {\overset{\sim}{\underset{\_}{x}}\lbrack n\rbrack}}}}\end{matrix}$

Exemplary techniques that can be utilized in a coefficient calculator410 to adaptively compute coefficients c to minimize the error signal{tilde over (e)}[n] include the Least Mean-Squares (LMS) and theRecursive Least-Squares (RLS). In some embodiments, the RLS may providefaster convergence and achieve performance that is somewhat independentof the input signal statistics. In exemplary embodiments, thecoefficient calculator 410 may iteratively compute, without requiringany matrix inversion, the coefficients c by compensation schemes,whether via LMS or RLS. The matrix inversion is computationallycumbersome and may introduce performance instability.

When using the LMS criterion, the coefficient calculator 410 computescoefficients iteratively as c[n+1]=c[n]+μ·{tilde over (x)}[n]·{tildeover (e)}*[n], where μ is a small number chosen to adjust an adaptationspeed.

When using the RLS criterion, the coefficient calculator 410 computescoefficients the iteratively as c[n+1]=c[n]+k[n]·{tilde over (e)}*[n],where λ is the forgetting factor, 0<λ≤1,

${{\underset{\_}{k}\lbrack n\rbrack} = \frac{\lambda^{- 1} \cdot {P\left\lbrack {n - 1} \right\rbrack} \cdot {\underset{\_}{\overset{\sim}{x}}\lbrack n\rbrack}}{1 + {\lambda^{- 1} \cdot {{\underset{\_}{\overset{\sim}{x}}}^{H}\lbrack n\rbrack} \cdot {P\left\lbrack {n - 1} \right\rbrack} \cdot {\underset{\_}{\overset{\sim}{x}}\lbrack n\rbrack}}}},$

and

P[n]=λ⁻¹ ·P[n−1]−λ⁻¹ ·k [n]· {tilde over (x)} ^(H)[n]·P[n−1]

PERFORMANCE STUDIES

Extensive simulations were implemented to evaluate the performance ofthe present teachings. The simulation setup used a highly efficientbroadband satellite application with high symbol rate of about 1Giga-Baud (GBaud) and data modulation that was high-order, based on32-ary amplitude phase-shift keying (32-APSK) constellation from theDVB-S2 and DVB-S2X standard. A pair of Root-Raised Cosine (RRC) filterswith a roll off factor of 0.05 served as interpolation and decimationfilters. The distortion was quantified in terms of the Mean SquaredError (MSE) between the received samples and the underlyingconstellations.

FIG. 5A illustrates real part of an impulse response of an RFI channelg₁[n] associated with a received signal according to variousembodiments. FIG. 5B illustrates imaginary part of an impulse responseof an RFI channel g₁[n] associated with a received signal according tovarious embodiments. FIG. 6A illustrates real part of an impulseresponse of an RFI channel g₂[n] associated with image of a receivedsignal according to various embodiments. FIG. 6B illustrates imaginarypart of an impulse response of an RFI channel g₂[n] associated withimage of a received signal according to various embodiments.

In the analog domain, a zero-IF quadrature down-conversion was used toproduce digital samples at a rate of 2 Gigahertz (GHz). The analoganti-aliasing filters h_(I)(t) and h_(Q)(t) were based on 6^(th)-orderButterworth criterion with a double-sided bandwidth of 1 GHz. Themismatch between these analog filters induces frequency-selective IQimbalance whose impulse responses are shown in FIG. 5A and FIG. 5B forg₁[n] and in FIG. 6A and FIG. 6B for g₂[n]. These figures illustratethat an induced frequency-selective imbalance channel for high datarates is strong and has a large time span.

The simulation environment included a frequency error δ_(ƒ) of 200Kilohertz (KHz) during training and 4 Megahertz (MHz) during normaloperation. The static gain and phase imbalance values, g and φ, were1.15 and 10°, respectively. Also, the DC-offset values injected forα_(DC,I) and α_(DC,Q) were 0.05 and −0.05, respectively.

FIG. 7 illustrates a representative transfer function of thecompensation filters w₁[n] and w₂[n] at the end of training for a RFIcompensator according to various embodiments.

FIG. 7 illustrates a representative transfer function of thecompensation filters, w₁[n] and w₂[n], computed at the end of theproposed training mode, for example per FIG. 12. The compensationfilters corrected for the signal linear distortion if present, asindicated by the 0 decibel (dB) error component, in a signal 702 in thefrequency-band of interest. The compensation filters also provided astrong rejection, as indicated by the almost −60 decibel (dB) null, ofan image signal 704 in the frequency-band of interest.

FIG. 8A illustrates a noiseless scatter plot of an output of a receiveRoot-Raised Cosine (RRC) filter without a RFI compensator according tovarious embodiments. FIG. 8B illustrates a noiseless scatter plot of anoutput of a receive RRC filter with an RFI compensator according tovarious embodiments.

FIG. 8A and FIG. 8B show noiseless scatterplots at the output of areceive RRC filter, with and without respectively, the RFI compensatorof the present teachings. FIG. 8A illustrates that the results withoutthe RFI compensator are unsatisfactory, per the more diffuse plotting,or clustering, of data points in FIG. 8A versus FIG. 8B, with distortionlevel at −16.7 dB, causing a performance error floor. In contrast, theRFI compensator used 13 taps in each arm and reduced the MSE by morethan 23 dB, essentially completely restoring IQ balance and suppressingDC offset in the presence of unavoidable frequency error.

FIG. 9 illustrates a simulated Mean Squared Error (MSE) at E_(s)/N₀=15dB with and without an RFI compensator according to various embodiments.

FIG. 9 reports the performance when Additive White Gaussian Noise (AWGN)contaminates the input r(t) of the quadrature-conversion architecture inFIG. 1. The Signal-to-Noise Ratio (SNR) is denoted as Es/N0, where Es issignal symbol energy and N0 is the one-sided power spectral densitylevel of the background noise. The levels of SNR are set at 33 dB fortraining and 15 dB during normal operation. The 15 dB value is typicalduring normal mode when employing 32 APSK constellation based on theDVB-S2X satellite standard. FIG. 10 compares the simulated performancein terms of MSE at the output of receive RRC filter with and without theproposed RFI compensator. Simulations indicate significant improvementrelative to systems not using the present teachings, with improvementsof more than 2 dB when using only 13 taps in each arm. Further, thepresent teachings completely and jointly remove the distortionsresulting from unavoidable analog RF impairments. These impairmentsinclude the frequency-independent IQ imbalance from the gain and phasemismatch of the LO mixer, frequency selective IQ imbalance from theanalog filters, and DC offset from LO carrier leakage. This excellentperformance is maintained even in the presence of frequency error of 4MHz.

The present teachings may be used at the transmitter and/or at thereceiver. In broadband satellite applications, a RFI compensator thataccounts for the RF impairments may typically be located at a remotereceiver. The present teachings are adaptive and do not require a prioriknowledge about the RF impairments impulse response. They operate asdata-aided at the factory where known signal {tilde over (z)}[n] usesknown training data during initial calibration. They can also operate ina decision-directed mode during normal operation to continuously trackcomponent variations due to temperature and aging, without sendingtraining data at a gateway from a remote terminal. Instead, the knownsignal {tilde over (z)}[n] in normal mode may use reliable sampleestimates generated by the demodulation process itself.

FIG. 10 illustrates a signal demodulation including an RFI compensatoraccording to various embodiments.

A receiver 1000 may include a tuner 1002 to receive an RF signal at acarrier frequency ƒ_(c). The RF signal is provided to an Analog toDigital Converter (ADC) 1104, whose output is provided to an RFIcompensator 1006. The output of the RFI compensator 1006 is provided toa demodulator 1008 to obtain a demodulated signal.

FIG. 11A illustrates a multi-carrier signal demodulation including aplurality of RFI compensators according to various embodiments.

A receiver 1100 may include a tuner 1102 to receive an RF signal at acarrier frequency ƒ_(c). The RF signal may be a multi-carrier signalincluding N signals having a carrier frequency of ƒ₁ to ƒ_(N). The RFsignal is provided to an Analog to Digital Converter (ADC) 1104, whoseoutput is provided to N RFI compensators 1106. Outputs of the N RFIcompensators 1106 are provided to N mixers 1110 to recover signalsmodulated at carrier frequencies from ƒ₁ to ƒ_(N). The signals modulatedat carrier frequencies ƒ₁ to ƒ_(N) are provided to N demodulators 1108to obtain N demodulated signals. In some embodiments, the N RFIcompensators 1106 are separately trained relative to the individualcarriers. In some embodiments, the N separately trained RFI compensators1106 are trained with different frequency errors δ_(ƒ).

FIG. 11B illustrates a multi-carrier signal demodulation including anRFI compensator according to various embodiments.

A receiver 1100′ may include a tuner 1102′ to receive an RF signal at acarrier frequency ƒ_(c). The RF signal may be a multi-carrier signalincluding N signals having a carrier frequency of ƒ₁ to ƒ_(N). The RFsignal is provided to an Analog to Digital Converter (ADC) 1104′, whoseoutput is provided to an RFI compensator 1106′. An output of the RFIcompensator 1106′ is provided to N mixers 1110′ to recover signalsmodulated at carrier frequencies from ƒ₁ to ƒ_(N). The signals modulatedat carrier frequencies ƒ₁ to ƒ_(N) are provided to N demodulators 1108′to obtain N demodulated signals. In some embodiments, the RFIcompensator 1106′ is trained relative to a wide frequency band thatincludes frequency bands of the N signals having the carrier frequenciesof ƒ₁ to ƒ_(N). In some embodiments, the RFI compensator 1106′ istrained relative to a wide frequency band that includes a singlewideband carrier. In some embodiments, the RFI compensator 1106′ trainedwith a frequency error δ_(ƒ) for the wide frequency band.

FIG. 12 illustrates a process for RFI compensation according to variousembodiments.

A RFI compensation process 1200 for RFI compensation may include aretrain subprocess 1228, a training mode 1202 and an operation mode1220.

The retrain subprocess 1228 may be used after deployment to train an RFIcompensator as needed. For example, the retrain subprocess 1228 can betriggered at operation 1230, The triggering may be in response to anelapsed time since last training exceeding a threshold, receiving apre-defined header from a transmitter such as a gateway, provisioning,initialization, or the like. In some embodiments, a header may include aPhysical Layer Signaling (PLS) code. The PLS code may be defined by astandard, such as, the DVB-S2 or DVB-S2X standard. In some embodiments,training of the RFI compensator may not be desired during signal fade.The retrain subprocess 1228 may check that a Signal-to-Noise Ratio (SNR)of a received signal is above a SNR threshold at operation 1232 beforeinitiating a training mode at operation 1234.

The training mode 1202 depends on having a known signal as a referencesignal, such as signal {tilde over (z)}[n] of FIG. 4. The RFIcompensation process 1200 includes providing a known signal at operation1204. The known signal may include a tone at a factory 1206 orextracting a known codeword 1208 with a fixed signal at deployment. Inexemplary embodiments, the known codeword 1208 may include a signal pera standard, such as, the DVB-S2 or DVB-S2X standard.

In training mode 1202 (see FIG. 4), the known signal and a receivedsignal, such as signal {tilde over (x)}[n] of FIG. 4, may then bealigned per operation 1209. The operation 1209 may align the knownsignal with the received signal for time, phase, gain or the like. Afteralignment, the RFI compensation process 1200 may add an estimated phaserotation 1210 to the known signal. The known and received signals areused to perform a stacked calculation of w₁[n], w₂[n], and optionally βat operation 1212 to obtain an RFI compensated signal, such as signal{tilde over (y)}[n] of FIG. 4. Operation 1212 may be performed usingknown filter methods such as Least Mean Squares at operation 1214, orRecursive Least Squares at operation 1216 to drive a difference/error(e[n] of FIG. 4) between the known signal and the RFI compensated signalto zero.

In operation mode 1220 (see FIG. 3), the RFI compensation process 1200includes filtering a received signal per w₁[n], w₂[n] at operation 1222.The RFI compensation process 1200 includes removing a DC Offset per β atoperation 1224. The RFI compensation process 1200 includes removing anestimated phase rotation at operation 1226.

Although the subject matter has been described in language specific tostructural features and/or methodological acts, it is to be understoodthat the subject matter in the appended claims is not necessarilylimited to the specific features or acts described above. Rather, thespecific features and acts described above are disclosed as exampleforms of implementing the claims. Other configurations of the describedembodiments are part of the scope of this disclosure. Further,implementations consistent with the subject matter of this disclosuremay have more or fewer acts than as described or may implement acts in adifferent order than as shown. Accordingly, the appended claims andtheir legal equivalents should only define the invention, rather thanany specific examples given.

I claim as my invention:
 1. A Radio Frequency Impairments (RFI)compensator comprising: a conjugator to conjugate a signal {tilde over(x)}[n] to provide a signal {tilde over (x)}*[n]; and a filter to applycoefficients that equalize a linear distortion of the signal {tilde over(x)}[n], and reject an interfering image of the signal {tilde over(x)}*[n].
 2. The RFI compensator of claim 1, further comprising acomplex mixer to remove an estimated frequency errore^(j2π{circumflex over (δ)}) ^(ƒ) ^(·nT) ^(s) from an output of thefilter.
 3. The RFI compensator of claim 1, further comprising an adderto add a voltage offset β to an output of the filter; and a complexmixer to remove an estimated frequency errore^(j2π{circumflex over (δ)}) ^(ƒ) ^(·nT) ^(s) from an adder output. 4.The RFI compensator of claim 1, wherein the signal {tilde over (x)}[n]comprises a multi-carrier signal comprising N signals having carrierfrequencies ƒ₁ to ƒ_(N), and N is greater than
 1. 5. The RFI compensatorof claim 4, wherein the filter comprises N filters and each of the Nfilters applies coefficients associated with a respective one of thecarrier frequencies ƒ₁ to ƒ_(N).
 6. The RFI compensator of claim 4,further comprising N complex mixers and N adders, wherein each of Nadders adds a DC offset β associated with a respective one of thecarrier frequencies ƒ₁ to ƒ_(N) from an output of a respective one ofthe N filters, and each of the N complex mixers removes an estimatedfrequency error e^(j2π{circumflex over (δ)}) ^(ƒ) ^(·nT) ^(s) associatedwith a respective one of the carrier frequencies ƒ₁ to ƒ_(N) from anoutput of a respective one the N adders.
 7. The RFI compensator of claim1, further comprising: a known signal {tilde over (z)}[n]; and acoefficient calculator to calculate coefficients for the filter based onthe known signal {tilde over (z)}[n] and the signal {tilde over (x)}[n],wherein the coefficients are based on the coefficients.
 8. The RFIcompensator of claim 7, wherein the coefficient calculator calculates avoltage offset β.
 9. The RFI compensator of claim 7, wherein thecoefficient calculator one or more of a Least Mean-Squares (LMS)technique or a Recursive Least-Squares (RLS) technique.
 10. The RFIcompensator of claim 7, further comprising a complex mixer to add anestimated frequency error e^(j2π{circumflex over (δ)}) ^(ƒ) ^(·nT) ^(s)to the known signal {tilde over (z)}[n].
 11. The RFI compensator ofclaim 7, wherein the coefficient calculator modifies the signal {tildeover (x)}[n] with the coefficients to generate a signal {tilde over(y)}[n] and iteratively calculates the coefficients to drive adifference between the known signal {tilde over (z)}[n] and the signal{tilde over (y)}[n] to zero.
 12. The RFI compensator of claim 7, whereinthe known signal comprises a reliable sample estimate generated by ademodulation.
 13. A process to compensate for Radio FrequencyImpairments (RFI), the process comprising: conjugating a signal {tildeover (x)}[n] to provide a signal {tilde over (x)}*[n]; and filtering byapplying coefficients that equalize a linear distortion of the signal{tilde over (x)}[n]and reject an interfering image of the signal {tildeover (x)}*[n].
 14. The process of claim 13, further comprising removingan estimated frequency error e^(j2π{circumflex over (δ)}) ^(ƒ) ^(·nT)^(s) from an output of the filtering.
 15. The process of claim 13,further comprising adding a voltage offset β to an output of thefiltering; and removing an estimated frequency errore^(j2π{circumflex over (δ)}) ^(ƒ) ^(·nT) ^(s) from an adding output. 16.The process of claim 13, wherein the signal {tilde over (x)}[n]comprises a multi-carrier signal comprising N signals having carrierfrequencies ƒ₁ to ƒ_(N), and N is greater than
 1. 17. The process ofclaim 16, wherein the filtering comprises N filters and each of the Nfilters applies coefficients associated with a respective one of thecarrier frequencies ƒ₁ to ƒ_(N).
 18. The process of claim 16, furthercomprising N complex mixers and N adders, wherein each of N adders addsa DC offset β associated with a respective one of the carrierfrequencies ƒ₁ to ƒ_(N) from an output of a respective one of the Nfilters, and each of the N complex mixers removes an estimated frequencyerror e^(j2π{circumflex over (δ)}) ^(ƒ) ^(·nT) ^(s) associated with arespective one of the carrier frequencies ƒ₁ to ƒ_(N) from an output ofa respective one of the N adders.
 19. The process of claim 13, furthercomprising: providing a known signal {tilde over (z)}[n]; andcalculating coefficients for the filtering based on the known signal{tilde over (z)}[n] and the signal {tilde over (x)}[n].
 20. The processof claim 19, wherein the calculating calculates a voltage offset β. 21.The process of claim 19, wherein the calculating comprises one or moreof a Least Mean-Squares (LMS) technique or a Recursive Least-Squares(RLS) technique.
 22. The process of claim 19, further comprising addingan estimated frequency error e^(j2π{circumflex over (δ)}) ^(ƒ) ^(·nT)^(s) to the known signal {tilde over (z)}[n].
 23. The process of claim19, wherein the calculating comprises modifying the signal {tilde over(x)}[n] with the coefficients to generate a signal {tilde over (y)}[n]and iteratively calculating the coefficients to drive a differencebetween the known signal {tilde over (z)}[n] and the signal {tilde over(y)}[n] to zero.
 24. The process of claim 19, wherein the known signalcomprises a reliable sample estimate generated by a demodulation.